Theorem simp3i 1142

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1139	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1088

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 398  df-3an 1090

This theorem is referenced by:  hartogslem2  9538  harwdom  9586  divalglem6  16341  structfn  17089  strleun  17090  oppchomfval  17658  sratset  20803  srads  20806  tngip  24162  dfrelog  26074  log2ub  26454  birthdaylem3  26458  birthday  26459  divsqrtsum2  26487  harmonicbnd2  26509  lgslem4  26803  lgscllem  26807  lgsdir2lem2  26829  lgsdir2lem3  26830  mulog2sumlem1  27037  siilem2  30105  h2hva  30227  h2hsm  30228  h2hnm  30229  elunop2  31266  wallispilem3  44783  wallispilem4  44784  prstchomval  47694